
Trigonometry Trigonometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
July 31st, 2015, 01:17 AM  #1 
Newbie Joined: Jun 2015 From: South Africa Posts: 27 Thanks: 0  Symmetry properties of graphs
In each of the following cases find the least positive value of α for which: a) cos(αθ)˚=sinθ˚ b) sin(αθ)˚=cos(α+θ)˚ There are a whole bunch more... I did a) easily because obviously cos(90θ)˚=sinθ˚, so α = 90. I'm struggling to work out b) though... Thanks for any help. 
July 31st, 2015, 04:50 PM  #2 
Math Team Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 
This is how I would do it. Simplifying $\sin(\alpha  \theta) = \cos(\alpha + \theta)$, we get $$ \sin(\alpha  \theta) = \cos(\alpha + \theta)\\ \sin\alpha\cos\theta  \sin\theta\cos\alpha = \cos\alpha\cos\theta  \sin\alpha\sin\theta\\ \sin\alpha(\cos\theta + \sin\theta) = \cos\alpha(\cos\theta + \sin\theta)\qquad\qquad\qquad(1) $$ In cases where $\cos\theta + \sin\theta = 0$, equality holds trivially. Otherwise, $(1)$ can be simplified to $$\sin\alpha = \cos\alpha,$$ or, $$\tan\alpha = 1.$$ We now see that the answer is $\alpha = 45^\circ$ 

Tags 
graphs, properties, symmetry 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
symmetry  mared  Algebra  1  January 27th, 2014 06:52 AM 
ODE's and symmetry groups  AfroMike  Abstract Algebra  0  October 24th, 2013 06:49 AM 
Question on isomorph Graphs and their complement Graphs  MageKnight  Applied Math  0  January 17th, 2013 10:38 PM 
Symmetry  ChristinaScience  Algebra  3  October 2nd, 2011 10:42 AM 